It is asserted in Lundbäck S., “Cardiac Pumping and Function of the Ventricular Septum”, Stockholm, 1986, that the pumping and regulation of the human heart take place in a manner which is at variance with the prevalent view. According to the cited publication, the healthy heart performs its pumping action without substantially changing its outer shape and volume. More particularly, during ventricular systole (the active, expulsive phase of the heart cycle) the so-called valve plane, that is, the plane containing the atrioventricular heart valves and the connections of aorta and pulmonary artery, is drawn towards the heart apex and forces the blood contained in the ventricles into the pulmonic and systemic circulation, and at the same time blood is drawn into the atria as a consequence of the movement of the valve plane. During ventricular diastole, the phase of the heart cycle in which the heart muscle is relaxed, the valve plane is returned to the initial position under the influence of the momentum which is imparted to the inflowing blood as a consequence of the downward movement of the valve plane during ventricular systole.
As is also asserted in the publication (on the basis of the finding that the outer volume and shape of the heart are substantially constant over the heart cycle), the ability of the heart to change the relative volumetric capacities of the right and left ventricles is attributable mainly to the common ventricular wall, the ventricular septum, namely by virtue of its flexibility in the relaxed state of the heart. During ventricular systole the ventricular septum together with the rest of the left ventricular musculature always assumes an essentially cross circular cross-sectional configuration and takes a distinct position independently of its shape and position during diastole. This is so, because during ventricular systole the pressure in the left ventricle is always higher than the pressure in the right ventricle. If the configuration and position of the ventricular septum during diastole, the relaxed state, are different from the configuration and position during systole, The active state, the ventricular septum, acting like a diaphragm pump, therefore provides an increased stroke volume for one ventricle and a correspondingly reduced stroke volume for the other ventricle, In this way, the ventricular septum accomplishes a double-acting regulation to maintain the balance between the two branches of the circulatory system (the pulmonary circulation and the systemic circulation).
As a result of the theory presented in above-mentioned publication regarding the heart's pumping and regulating function a new class of pumps has emerged, a so called dynamic displacement pump or delta (Δ) volume pump (abbreviated as ΔV-pump).
The principles of a ΔV-pump will now be described with references to FIGS. 1a and 1b. 
The pump comprises an upper cylinder 2 with diameter d1 and a lower cylinder 4 with diameter d2, where d2>d1. These two cylinders are connected to each other via a third cylinder 6 that is freely movably arranged between the upper and lower cylinders. The movable cylinder 6 is provided with a valve 8 at its lowest part that corresponds e.g. to the mitralis valve in the heart. The volume above this valve is defined as the atrial volume (Va) and the volume below the valve is defined as the ventricular volume (Vv). The lower cylinder is provided with an outflow valve 10 at its lowest part that corresponds e.g. to the aortic valve in the heart. As can be seen from FIG. 1b is a ring-shaped cylindrical volume gradually obtained between the movable cylinder and the inner wall of the lower cylinder when the movable cylinder is moved down, ΔV in the figure. This results in that the volume Va+Vv decreases with the volume ΔV when the movable cylinder moves between its upper position and its lower position. A source of energy (not shown in the figures) is adapted to move the movable cylinder from its upper position to its lower position, which defines the length L of a stroke for the pump. When the movable cylinder moves down to its lowest position the outflow valve is forced to open and a part of volume Vv is expelled. The movable cylinder is then released from the source of energy and can return to its upper position. If Av and Aa designates the cross-sectional areas of the upper and lower cylinder, respectively, ΔV equals L(Av−Aa).
A short description of the behavior of the ΔV-pump when pumping with a lower frequency and with a higher frequency will here follow, with references to FIGS. 2 and 3 respectively.
In FIGS. 2a-2d different stages of the pumping process with a low frequency are disclosed. In FIG. 2a the external force starts moving the movable cylinder down, when the pressure inside the lower cylinder exceeds the pressure below the outflow valve 10 it opens (FIG. 2b). The outflow valve closes when the pressure below the valve exceeds the pressure above. When the movable cylinder is in the lowest position the force activation ends and the fluid in the upper cylinder, which has gained kinetic energy downwards, force the valve 8 to open (FIG. 2c). The inflow in the lower cylinder creates an internal redistribution of the fluid, indicated by the arrows, that firstly forces the freely movable cylinder back to the upper position and secondly creates the necessary pressure to close the valve 8 (FIG. 2d). The reason to this is the different diameters of the upper and lower cylinders resulting in that the movable cylinder has a greater area towards volume Vv than towards volume Va. When these areas are exposed to the same pressure the force towards the upper position will be greater due to the greater area. This in turn results in that the inflow continues even when the outflow has stopped.
In FIGS. 3a-3d different stages of the pumping process with a high frequency are disclosed. FIG. 3a illustrates only the starting position whereas the pumping process with a high frequency is illustrated by FIGS. 3b-3d. The differences from the pumping process with a low frequency are illustrated in FIGS. 3c and 3d. The downward kinetic energy is in this case so large that both valves are opened when the movable cylinder reaches the lower position. The valves are then closed due to the same reasons as when pumping with low frequency.
Many different requirements must generally be met when implementing a mathematical model. It should preferably be module based in order to be easy to modify, to monitor, to error detect and to control. It is also important that different physical systems, such as mechanical, electrical, thermal and hydraulic systems easily can be connected together and it must be possible to control and to monitor any part of the model when at work.
In order to describe graphically a system with different physical domains the so called bond graphs has proven to be a powerful tool. Bond graphs was introduced by H. Paynter at the MIT and is e.g. described in Karnopp, Margolis, Rosenberg, “System Dynamics: A Unified Approach” (second edition) and in Thoma, Jean U. “Simulation by Bond graphs, introduction to a Graphical Method”; Springer-Verlag.
The basics for a systematic modeling using bond graphs are essentially to follow the energy flow through the system(s).
One object of the invention is to be able to simulate the function of a ΔV-pump.
One further object of the invention is to be able to simulate the functions of a heart by using a mathematical model of the functions of the heart based upon the above-described principles of the ΔV-pump in order to make it possible to enhance the methods of analyses, diagnosis and therapy of the heart.